Introduction to volume of rectangular prisms

Introduction to volume of rectangular prisms

Lessons

In this lesson, we will learn:

  • The relationship between 3-dimensional shapes, cubic measure, and the 3D geometric property of volume
  • How to use the formula for volume of rectangular prisms: V=l×w×h V = l \times w \times h

Notes:

  • Volume is the 3-dimensional (3D) property of a geometric shape
    • Volume represents the amount of space occupied by a 3D shape
    • Volume is created by the combination of three dimensions (three different planes/directions of measurement)
    • Cubic measure (cubic units) is used to measure volumes of 3D shapes
      • Some examples of cubic units are: m3, cm3, mm3; ft3, in3, yd3

2D Shapes: Area and Perimeter of Rectangles

  • For the geometric properties of shapes:

2D Shapes: Area and Perimeter of Rectangles

    • A 2D shape has the 2D property of area and the 1D property of perimeter
    • A 3D shape has the 3D property of volume and the 2D property of surface area
  • The volume (VV) for a rectangular prism combines the three dimensions of: length (ll), width (ww), and height (hh) and can be found using the formula:
    • V=l×w×hV = l \times w \times h
2D Shapes: Area and Perimeter of Rectangles
  • Introduction
    Introduction to Introduction to Volume of Rectangular Prisms:
    a)
    What is volume and why do we use cubic units for volume?

    b)
    What is the volume formula and how do you define length, width, and height?

    c)
    How to calculate volume using the volume formula for a rectangular prism

    d)
    How to calculate


  • 1.
    Volume with Cubic Unit Blocks
    Find the length, width, height, and volume for the 3D shape
    a)

    2D Shapes: Area and Perimeter of Rectangles

    b)

    2D Shapes: Area and Perimeter of Rectangles

    c)

    2D Shapes: Area and Perimeter of Rectangles


  • 2.
    Volume of Rectangular Prisms
    Find the volume of the rectangular prism using the formula V=l×w×hV =l \times w \times h
    a)

    2D Shapes: Area and Perimeter of Rectangles

    b)

    2D Shapes: Area and Perimeter of Rectangles

    c)

    2D Shapes: Area and Perimeter of Rectangles


  • 3.
    Manipulating Volume Equation for Rectangular Prisms
    Solve for the missing measurement of each rectangular prism
    a)

    2D Shapes: Area and Perimeter of Rectangles

    b)

    2D Shapes: Area and Perimeter of Rectangles

    c)

    2D Shapes: Area and Perimeter of Rectangles


  • 4.
    Word Problem - Volume of Rectangular Prisms
    Pizza boxes all have a square base and a height of 2 inches.
    a)
    What is the volume of a large pizza box that is 15 inches long, 15 inches wide, and 2 inches high?

    b)
    What is the length and width of the small pizza box if the volume is 162 in3?

    c)
    If you ordered 2 large pizzas and 1 small pizza, what is the total volume of boxes stacked together when it arrives?